## Am I doing this correctly? - Z test

I am working on a practice problem for my behavioral science statistics class. My work is in bold.

Using the following data:
University undergraduate GPA: µ= 2.91 est. σ= .71
Class GPA: Xbar = 3.31 s=.69 n=12
My GPA: 2.9

1. I have been asked to test the following hypothesis: is this class significantly different from the university undergrads? Using α=.10 (yes, .10 not .01).

I have determined:
Ho: X = µ
Ha: X ≠ µ

Compute critical z('s) or critical GPA(s):

standard error of the mean:
.69/√12 = .69/3.46 = .20

z= 3.31 - 2.91/.20 = .4/.20 = 2.0

z (critical z, .05% below/above)
= ±2.32

I was a bit confused about how to determine the critical z, as my instructor and text were unclear about examples using alpha = anything besides the "usual" .05.

State your statistical decision to reject or fail to reject Ho:
Fail to reject Ho.

2. Assuming grades at the university are normally distributed, what is the percentile of your GPA?

--- I have an equation to determine percentile using cumulative frequency (using LRL and such), but I am unsure if this is the correct formula to use for this problem.

>> I am fairly certain that I am making at least a few mistakes on this, but I am interested in learning how to perform the test correctly.

Sorry about all the reading in this post, but I am grateful for all input. Any and all assistance will be greatly appreciated. Thank you in advance. I really want to learn how to do this!